Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used (...) to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, meta-level attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data). (shrink)

To create a programming environment for contract dispute resolution, we propose an extension of assumption-based argumentation into modular assumption-based argumentation in which different modules of argumentation representing different knowledge bases for reasoning about beliefs and facts and for representation and reasoning with the legal doctrines could be built and assembled together. A distinct novel feature of modular argumentation in compare with other modular logic-based systems like Prolog is that it allows references to different semantics in the same module at the (...) same time, a feature critically important for application of argumentation in legal domains like contract dispute resolution where the outcomes of court cases often depend on whether credulous or skeptical modes of reasoning were applied by the contract parties. We apply the new framework to model the doctrines of contract breach and mutual mistake. (shrink)

We provide a logical analysis of private international law, a rather esoteric, but increasingly important, domain of the law. Private international law addresses overlaps and conflicts between legal systems by distributing cases between the authorities of such systems (jurisdiction) and establishing what rules these authorities have to apply to each case (choice of law). A formal model of the resulting interactions between legal systems is proposed based on modular argumentation. It is argued that this model may also be useful for (...) governing the interactions between heterogeneous agents, belonging to different and differently regulated virtual societies, without recourse to a central regulatory agency. The model also provides for multiple interpretations concerning rules of private international law as well as substantive rules of the different legal systems. (shrink)

In the court of law, a person can be punished for attempting to commit a crime. An open issue in the study of Artificial Intelligence and Law is whether the law of attempts could be formally modelled. There are distinct legal rules for determining attempted crime whereas the last-act rule (also called proximity rule) represents the strictest approach. In this paper, we provide a formal model of the last-act rule using structured argumentation.